Solve $\dfrac{x}{4} \gt \dfrac{5x - 2}{3} - \dfrac{7x - 3}{5}$, x ∈ R. Also represent the solution set on the number line.

Solving,

$\Rightarrow \dfrac{x}{4} \gt \dfrac{5x - 2}{3} - \dfrac{7x - 3}{5} \\[1em] \Rightarrow \dfrac{x}{4} \gt \dfrac{5(5x - 2) - 3(7x - 3)}{15} \\[1em] \Rightarrow \dfrac{x}{4} \gt \dfrac{25x - 10 - 21x + 9}{15} \\[1em] \Rightarrow \dfrac{x}{4} \gt \dfrac{4x - 1}{15} \\[1em]$

Multiplying both sides by 60, we get :

$\Rightarrow \dfrac{x}{4} \times 60 \gt \dfrac{4x - 1}{15} \times 60 \\[1em] \Rightarrow 15x \gt 4(4x - 1) \\[1em] \Rightarrow 15x \gt 16x - 4 \\[1em] \Rightarrow 16x - 15x \lt 4 \\[1em] \Rightarrow x \lt 4.$

Hence, solution set is {x : x ∈ R and x < 4}.